Interest in dielectric barrier discharges (DBD) “plasma actuators” for flow control has seen a tremendous growth in the past 15 years in the U.S. and around the world. The reasons for this are likely based on their special features that include being fully electronic with no moving parts, having a fast response time for unsteady applications, having a very low mass which is especially important in applications with high g-loads, being able to apply the actuators onto surfaces without the addition of cavities or holes, having an efficient conversion of the input power without parasitic losses when properly optimized, and the easy ability to simulate their effect in numerical flow solvers.
The predominant DBD configuration used for flow control consist of two electrodes, one uncoated and exposed to the air and the other encapsulated by a dielectric material. For plasma actuator applications, the electrodes are generally arranged in a highly asymmetric geometry.
Referring to FIG. 1, an example configuration for an alternative current (AC) set-up for a prior art AC plasma actuator 10 is shown in FIG. 1. For the AC-DBD operation, the electrodes 102 and 104 are supplied with an AC voltage from the power source 112 that, at high enough levels, causes the air over the covered electrode to weakly ionize. This is typically less than 1 PPM weakly ionized gas. The ionized air appears blue, which is a characteristic of the composition of the air as ionized components of the air recombine and de-excite. The emission intensity is extremely low, requiring a darkened space to view by eye.
The ionized air, in the presence of the electric field produced by the geometry of electrodes 102 and 104, results in a body force vector field that acts on the ambient (non-ionized, neutrally charged) air or other fluid. The body force can be used as a mechanism for active aerodynamic control. In determining the response of the ambient air, the body force appears as a term on the right-hand-side of the fluid momentum equation.
For a single dielectric barrier discharge (SDBD), during one-half of the AC cycle, electrons leave the metal electrode and move towards the dielectric where they accumulate locally. In the reverse half of the cycle, electrons are supplied by surface discharges on the dielectric and move toward the metal electrode. The time scale of the process depends on the gas composition, excitation frequency, and other parameters. In air and at atmospheric pressure, it occurs within a few tens of nanoseconds.
Although the generated plasma is composed of charged particles, it is net neutral because it is created by the ionization of neutral air and an equal number of negative electrons and positive ions exist in the plasma. The charged particles respond to the external electric field, and the electrons move to the positive electrode and the positive ions move to the negative electrode. This movement results in an imbalance of charges on the edges of the plasma that sets up an electric field in the plasma that is opposite to the externally applied electric field. The imbalance of charges on the edges of the plasma is due to the thermal motion of the charged particles in the plasma. The rearrangement of the charged particles continues until the net electric field in the plasma is neutralized.
Enloe et al. studied the space-time evolution of the ionized air light-emission over a surface mounted SDBD plasma actuator using a photo-multiplier tube (PMT) fitted with a double-slit aperture to focus on a narrow 2-D region of the plasma. (Enloe, L. et al., “Mechanisms and Responses of a Single-Dielectric Barrier Plasma Actuator: Plasma Morphology.” AIAA, Vol. 42, 2004, pp. 589-594.) The slit was parallel to the edge of the exposed electrode and could be moved to different locations over the other electrode that was covered by the dielectric.
FIG. 2 shows a sample time series of the results from Orlov. (Orlov, D. M., Modelling and Simulation of Single Dielectric Barrier Discharge Plasma Actuators, Ph.D. thesis, University of Notre Dame, 2006.) The top graph is a visualization of the of the PMT output that was acquired phase-locked with the AC input to the actuator. The lower portion of FIG. 2 shows the AC input supplied to the electrodes over the same time period. The light emission is taken as an indication of the plasma density, which is a good assumption based on the disparate time scales between the recombination time (order of 10−8 sec) versus the discharge time scale (order of 10−3 sec).
The explanation for the difference in the emission character in the two half-cycles shown in FIG. 2 is associated with the source of electrons. During the negative-going half cycle, the electrons originate from the bare electrode, which is essentially an infinite source that readily gives them up. In the positive-going half cycle, the electrons originate from the dielectric surface. These apparently do not come off as readily, or when they do, they come in the form of fewer, larger micro-discharges. This asymmetry has been modeled by Boeuf and Orlov and plays an important role in the efficiency of the momentum coupling to the neutrals. (Boeuf, J. et al. “Electrohydrodynamic force in dielectric barrier discharge plasma actuators.” J. Phys. D.: Appl. Phys., Vol. 40, 2007, pp. 652-662; Orlov, D., Font, G., and Edelstein, D., “Characterization of Discharge Modes of Plasma Actuators.” AIAA J., Vol. 46, 2008, pp. 3142-3148.) It further suggests some optimization can come in the selection of the AC waveform to improve the performance of the plasma actuator.
Wall-mounted AC plasma actuators 10 with an asymmetric electrode design like that shown in FIG. 1, induce a velocity field similar to that of a tangential wall jet. Enloe et al. correlated the reaction force (thrust) generated by the induced flow with the actuator AC amplitude. (Enloe, L., McLaughlin, T., VanDyken, Kachner, Jumper, E., Corke, T., Post, M., and Haddad, O., “Mechanisms and Responses of a Single-Dielectric Barrier Plasma Actuator: Geometric Effects.” AIAA, Vol. 42, 2004, pp. 595-604.) A similar experiment was performed by Thomas et al. to investigate parameters in the actuator design. (Thomas, F. et al., “Optimization of SDBD Plasma Actuators for Active Aerodynamic Flow Control,” AIAA J., Vol. 47-9, 2010, pp. 2169-2177.) At the lower voltages, the induced thrust of the AC plasma actuator 10 was found to be proportional to V3:5 AC. This was first observed by Enloe et al. (“Geometric Effects.”) Thomas et al. verified consistency between the reaction force and the fluid momentum by integrating the velocity profiles downstream of the actuator. (“Optimization of SDBD Plasma Actuators”) Post found that the maximum induced velocity was proportional to V3:5 AC, which is consistent with conserved momentum in the self-similar velocity profile region near the actuator. (Post, M. L., “Plasma actuators for separation control on stationary and unstationary airfoils” Ph.D. thesis, University of Notre Dame, 2004.) At the highest voltages, the thrust change with voltage still appears to follow a power law relation, although the exponent is smaller and not necessarily universally accepted. The voltage at which the power-law exponent changes is a function of the area of the covered electrode, with a smaller area causing the change to occur at lower voltages.
As indicated, the body force produced by AC-DBD plasma actuators occurs over a relatively short portion of the two-halves of the AC cycle. In addition, only the portion where the electrons leave the exposed electrode to be deposited onto the dielectric surface, contributes the significant amount of the net body force. This process of the AC body force generation is often referred to as “big push, little push.” It is known that at larger static pressures, with atmospheric pressure being considered part of that set, it is easier to ionize the air using AC. Ionizing the air makes it conductive and thereby responsive to the electric field.